Cryptology ePrint Archive: Report 2002/106

Secret sharing schemes on access structures with intersection number equal to one

Jaume Marti-Farre and Carles Padro

Abstract:
The characterization of ideal access structures and
the search for bounds on the optimal information rate
are two important problems in secret sharing.
These problems are studied in this paper for access structures
with intersection number equal to one, that is, access structures
such that there is at most one participant in the intersection
of any two different minimal qualified subsets.
The main result in this work is the complete characterization
of the ideal access structures with intersection number equal to one.
Besides, bounds on the optimal information rate
are provided for the non-ideal case.